corrcal

corrcal is a calibration tool for radio interferometers that utilises the Correlation Calibration scheme developed in Sievers 2017). This particular repository is being collaboratively developed to improve upon the original repository provided in Sievers 2017.

Scientific Motivation

corrcal aims to bridge the gap between traditional sky based and redundancy based calibrations. Both extremes of calibrations rely on inherently incorrect assumptions:

• Sky based calibration relies on perfect sky models
• Redundant calibration relies on identical baselines

Both are, therefore, not realistic. corrcal overcomes this by:

• relaxing the assumption of perfect redundancy
• enabling the inclusion of partial sky knowledge

It does so by describing visibility correlations, due to quasi-redundancy or foreground sources, with a covariance matrix C and reformulating the calibration problem as the following chi-square minimization:

    

• d is the observed complex visibility (data) vector
• G is the complex gain matrix
• N is thermal noise matrix

This minimization requires efficient matrix inversion, which is achieved through Cholesky factorisation and the Woodbury identity.

Installation

Clone this repository,

git clone https://github.com/UKZN-Astronomy/corrcal.git

then cd into the cloned directory, and install through pip

pip install .

Usage

Once code is set up, the important thing needed to run on ones data is to get the sparse matrix describing sky and source correlations set up. Please take a look at read_sparse in corrcal.py for an example of how the matrix is structured. A convenient function to convert pyuvdata object to corrcal sparse matrix is planned. In short, the sparse matrix format groups visibilities into redundant blocks and separate the real and imaginary parts following their respective reals.

The important fields in the spare matrix object are: diag: the noise variance of visibilities lims: the indices that set off the redundant blocks. vecs: the vectors describing the sky covariances within blocks. It's currently assumed that the number of vectors is the same for each block. If you don't want this, you can zero-pad. src: the per-visibility response to sources with known positions. isinv: is the covariance matrix an inverse. You will start with this flag set to False.

When you have these in place, you can create a sparse matrix with

mat = corrcal.sparse_2level(diag, vecs, src, lims, isinv)

Note that if you want to run with classic redundant calibration, the source vector will be zeros, and the sky vectors will be some large number times

[1 0 1 0 1 0 1 0...
 0 1 0 1 0 1 0 1....]

which says there's random signal in the real visibilities which is uncorrelated with the imaginary visibilities.

To run, you will also need to get data and per-visibility antenna 1/antenna 2 (assumed zero-offset indexing on the antennas) read in, plus a guess at the initial gains. Then you can fit for gains with the scipy non-linear conjugate gradient solver (from scipy.optimize import fmin_cg). One final wrinkle is that scipy often tries trial steps far too large for the gain errors, causing matrix to go non-positive definite. If you hit this, you can set a scale factor to some large number until the minimizer behaves. Look in corrcal_example.py (which runs a whole PAPER-sized problem) to see how this works.

Contribution

corrcal is currently undergoing an active development and enhancement. The current maintainers are:

• Piyanat Kittiwisit (University of KwaZulu-Natal)
• Ronniy Joseph (Curtin University)

with supervisation form Jonathan Sievers (University of KwaZulu-Natal and McGill University)

All contribution or suggestion are welcome. We are particularlly looking for more codes developers.